Question

The number of permutations of the word $AUROBIND$ in which vowels appear in the alphabetical order, is

• A. ${}^8{P}_4$
• B. ${}^8{C}_4$
• C. $4!\times {}^8{C}_4$
• D. $5!\times {}^8{C}_5$

Answer 1

Answer: (A), (C)

The correct options are
A ${}^8{P}_4$
C $4!\times {}^8{C}_4$

There are four vowels, $A,U,O,I$
We first choose four positions to put these four vowels in alphabe order. This can be done in ${}^8{C}_4$ ways.
Now, the remaining four positions can be filled by the four consonants in $4!$ ways.
Hence, required number of permutations $={}^8{C}_4\times 4!={}^8{P}_4$